• Preface; Notation; Part I. Special Relativity: 1. Introduction: inertial systems and Galilei invariance of classical mechanics; 2. Light propagation in moving coordinate systems and Lorentz transformations; 3. Our world as a Minkowski space; 4. Mechanics of special relativity; 5. Optics of plane waves; 6. Four-dimensional vectors and tensors; 7. Electrodynamics in vacuo; 8. Transformation properties of electromagnetic fields: examples; 9. Null vectors and the algebraic properties of electromagnetic field tensors; 10. Charged point particles and their field; 11. Pole-dipole particles and their field; 12. Electrodynamics in media; 13. Perfect fluids and other physical theories; Part II. Riemannian Geometry: 14. Introduction: the force-free motion of particles in Newtonian mechanics; 15. Why Riemannian geometry?; 16. Riemannian space; 17. Tensor algebra; 18. The covariant derivative and parallel transport; 19. The curvature tensor; 20. Differential operators, integrals and integral laws; 21. Fundamental laws of physics in Riemannian spaces; Part III. Foundations of Einstein's Theory of Gravitation: 22. The fundamental equations of Einstein's theory of gravitation; 23. The Schwarzschild solution; 24. Experiments to verify the Schwarzschild metric; 25. Gravitational lenses; 26. The interior Schwarzschild solution; Part IV. Linearized Theory of Gravitation, Far Fields and Gravitational Waves: 27. The linearized Einstein theory of gravity; 28. Far fields due to arbitrary matter distributions and balance equations for momentum and angular momentum; 29. Gravitational waves; 30. The Cauchy problem for the Einstein field equations; Part V. Invariant Characterization of Exact Solutions: 31. Preferred vector fields and their properties; 32. The Petrov classification; 33. Killing vectors and groups of motion; 34. A survey of some selected classes of exact solutions; Part VI. Gravitational Collapse and Black Holes: 35. The Schwarzschild singularity; 36. Gravitational collapse - the possible life history of a spherically symmetric star; 37. Rotating black holes; 38. Black holes are not black - relativity theory and quantum theory; 39. The conformal structure of infinity; Part VII. Cosmology: 40. Robertson-Walker metrics and their properties; 41. The dynamics of Robertson-Walker metrics and the Friedmann universes; 42. Our Universe as a Friedmann model; 43. General cosmological models; Bibliography; Index.

'All in all this is an impressive range of topics to cover in an introductory survey which starts more or less from scratch … The mathematical treatment is rigorous but perfectly accessible to physics and applied mathematics students in their third or fourth years. … It can be recommended, not only to students of relativity but to astrophysicists, cosmologists and particle physicists. It would also be of great use to physicists from other fields, at all levels, not attending a formal course, but rather interested in getting to grips with the subject by private study.' Contemporary Physics

• Preface; Notation; Part I. Special Relativity: 1. Introduction: inertial systems and Galilei invariance of classical mechanics; 2. Light propagation in moving coordinate systems and Lorentz transformations; 3. Our world as a Minkowski space; 4. Mechanics of special relativity; 5. Optics of plane waves; 6. Four-dimensional vectors and tensors; 7. Electrodynamics in vacuo; 8. Transformation properties of electromagnetic fields: examples; 9. Null vectors and the algebraic properties of electromagnetic field tensors; 10. Charged point particles and their field; 11. Pole-dipole particles and their field; 12. Electrodynamics in media; 13. Perfect fluids and other physical theories; Part II. Riemannian Geometry: 14. Introduction: the force-free motion of particles in Newtonian mechanics; 15. Why Riemannian geometry?; 16. Riemannian space; 17. Tensor algebra; 18. The covariant derivative and parallel transport; 19. The curvature tensor; 20. Differential operators, integrals and integral laws; 21. Fundamental laws of physics in Riemannian spaces; Part III. Foundations of Einstein's Theory of Gravitation: 22. The fundamental equations of Einstein's theory of gravitation; 23. The Schwarzschild solution; 24. Experiments to verify the Schwarzschild metric; 25. Gravitational lenses; 26. The interior Schwarzschild solution; Part IV. Linearized Theory of Gravitation, Far Fields and Gravitational Waves: 27. The linearized Einstein theory of gravity; 28. Far fields due to arbitrary matter distributions and balance equations for momentum and angular momentum; 29. Gravitational waves; 30. The Cauchy problem for the Einstein field equations; Part V. Invariant Characterization of Exact Solutions: 31. Preferred vector fields and their properties; 32. The Petrov classification; 33. Killing vectors and groups of motion; 34. A survey of some selected classes of exact solutions; Part VI. Gravitational Collapse and Black Holes: 35. The Schwarzschild singularity; 36. Gravitational collapse - the possible life history of a spherically symmetric star; 37. Rotating black holes; 38. Black holes are not black - relativity theory and quantum theory; 39. The conformal structure of infinity; Part VII. Cosmology: 40. Robertson-Walker metrics and their properties; 41. The dynamics of Robertson-Walker metrics and the Friedmann universes; 42. Our Universe as a Friedmann model; 43. General cosmological models; Bibliography; Index.

'All in all this is an impressive range of topics to cover in an introductory survey which starts more or less from scratch … The mathematical treatment is rigorous but perfectly accessible to physics and applied mathematics students in their third or fourth years. … It can be recommended, not only to students of relativity but to astrophysicists, cosmologists and particle physicists. It would also be of great use to physicists from other fields, at all levels, not attending a formal course, but rather interested in getting to grips with the subject by private study.' Contemporary Physics

• Preface; Notation; Part I. Special Relativity: 1. Introduction: inertial systems and Galilei invariance of classical mechanics; 2. Light propagation in moving coordinate systems and Lorentz transformations; 3. Our world as a Minkowski space; 4. Mechanics of special relativity; 5. Optics of plane waves; 6. Four-dimensional vectors and tensors; 7. Electrodynamics in vacuo; 8. Transformation properties of electromagnetic fields: examples; 9. Null vectors and the algebraic properties of electromagnetic field tensors; 10. Charged point particles and their field; 11. Pole-dipole particles and their field; 12. Electrodynamics in media; 13. Perfect fluids and other physical theories; Part II. Riemannian Geometry: 14. Introduction: the force-free motion of particles in Newtonian mechanics; 15. Why Riemannian geometry?; 16. Riemannian space; 17. Tensor algebra; 18. The covariant derivative and parallel transport; 19. The curvature tensor; 20. Differential operators, integrals and integral laws; 21. Fundamental laws of physics in Riemannian spaces; Part III. Foundations of Einstein's Theory of Gravitation: 22. The fundamental equations of Einstein's theory of gravitation; 23. The Schwarzschild solution; 24. Experiments to verify the Schwarzschild metric; 25. Gravitational lenses; 26. The interior Schwarzschild solution; Part IV. Linearized Theory of Gravitation, Far Fields and Gravitational Waves: 27. The linearized Einstein theory of gravity; 28. Far fields due to arbitrary matter distributions and balance equations for momentum and angular momentum; 29. Gravitational waves; 30. The Cauchy problem for the Einstein field equations; Part V. Invariant Characterization of Exact Solutions: 31. Preferred vector fields and their properties; 32. The Petrov classification; 33. Killing vectors and groups of motion; 34. A survey of some selected classes of exact solutions; Part VI. Gravitational Collapse and Black Holes: 35. The Schwarzschild singularity; 36. Gravitational collapse - the possible life history of a spherically symmetric star; 37. Rotating black holes; 38. Black holes are not black - relativity theory and quantum theory; 39. The conformal structure of infinity; Part VII. Cosmology: 40. Robertson-Walker metrics and their properties; 41. The dynamics of Robertson-Walker metrics and the Friedmann universes; 42. Our Universe as a Friedmann model; 43. General cosmological models; Bibliography; Index.

'All in all this is an impressive range of topics to cover in an introductory survey which starts more or less from scratch … The mathematical treatment is rigorous but perfectly accessible to physics and applied mathematics students in their third or fourth years. … It can be recommended, not only to students of relativity but to astrophysicists, cosmologists and particle physicists. It would also be of great use to physicists from other fields, at all levels, not attending a formal course, but rather interested in getting to grips with the subject by private study.' Contemporary Physics